# Lecture Notes for STAT 2004 - Introductory Statistics at Virginia Tech (VT)

## Notes Information

 Material Type: CribSheet Professor: Staff Class: STAT 2004 - Introductory Statistics Subject: Statistics University: Virginia Polytechnic Institute And State University Term: Spring 2006 Keywords: No CorrelationAchievementSample CorrelationStrong CorrelationRelationshipObservationLinear RelationshipInterpretationPositive CorrelationCorrelation Coefficient (r) ## Sample Document Text

10.1 THE LINEAR CORRELATION COEFFICIENT • Sample correlation coefficient, r, is measure of degree of linear relationship between two variables in the sample • Formula : r= Sxy/SxSy where Sxy= [(X-X)(Y-Y)]/n-1 * Different from formula in book (ignore formulas in book) 10.2 EXAMPLE: "BEHAVIOR AND ACHIEVEMENT" As part of a study on grade school children, a researcher wanted to investigate the relationship between behavior in school (X) and an index of academic achievement (Y). Compute the sample correlation coefficient using the following data for five randomly selected children. Behavior (X) Achievement (Y) 7 15 1 7 14 12 3 5 5 11 X Y (X-X) (X-X)^2 (Y-Y) (Y-Y)^2 (X-X) (Y-Y) 7 15 1 1 5 25 5 17 –5 25 –3 9 15 14 12 8 64 2 4 16 35 –3 9 –5 25 15 5 11 –1 1 1 1 –1 30 50 0 100 0 64 50 Values of r • Range: –1 ≤ r ≤ +1 • Positive correlation (r > 0) * High values on X tend to go with high values on Y, Low values on X with low values on Y * Plot (X,Y) points: best-fitting line slopes up to right ...

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